It takes a dire situation for an Australian cricket team to write itself off, but coach Darren Lehmann has admitted Australia's best hope at the MCG is a draw.

Alastair Cook's remarkable, unbeaten 244 — in combination with half-centuries from Joe Root and Stuart Broad — has taken the game away from the hosts after only three days of the fourth Test, with England's lead out to 164 at the close of play on Wednesday.

Though famously a very positive and aggressive coach, Lehmann admits the game is now beyond Australia.

"It's tough to see any other scenario other than a draw or England win," Lehmann said.

"It's going to take us a long time to get past them, to be perfectly honest. So really our job is to bat a lot of overs and do exactly what they've just done to us.

"For us, you never say never, but we're a long way behind in the game, so for us it's about batting as long as we possibly can, and see where the game takes us."

The Australian bowlers have toiled for the best part of two days for little reward, struggling to extract life from a pitch that has faced criticism for its lifelessness.

Lehmann felt sympathy for his bowlers, who he said tried everything throughout day three to find something in the wicket.

"We tried, it was really hard. Obviously it's not going through at all," he said.

"Broad got 56 and we couldn't really do too much there either — we tried to bounce him as much as we possibly can, but if there's no pace in the wicket it makes it hard.

"So when you've got quicks like Cummins who can't get it up it makes it a bit hard, but then you've got to bowl tight as well.

"You'd like a bit more pace and bounce in it, there's no doubt about that."

But despite Australia's struggles, Lehmann was most keen to praise the batting of Cook.